arXiv subjects

Yasunori Okada

Publications and source records attributed to Yasunori Okada.

4 recordsLinked to original sources

arXiv2024

Asymptotic Expansions of Finite Hankel Transforms and the Surjectivity of Convolution Operators

A compactly supported distribution is called invertible in the sense of Ehrenpreis-Hörmander if the convolution with it induces a surjection from $\mathcal{C}^{\infty}(\mathbb{R}^{n})$ to itself. We give sufficient conditions for radial functions to be invertible. Our analysis is based on the asymptotic expansions of finite Hankel transforms. The dominant term may be the contribution from the origin or from the boundary of the support of the function. For the proof, we propose a new method to calculate the asymptotic expansions of finite Hankel transforms of functions with singularities at a point other than the origin.

math.FA↗

arXiv2020

A differential operator representation of continuous homomorphisms between the spaces of entire functions of given proximate orders

In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a corollary, we give a characterization of continuous endomorphisms of such spaces.

math.FA↗

arXiv2020

Generalized spherical mean value operators on Euclidean space

We consider the Neumann version of the spherical mean value operator and its variants in the space of smooth functions, distributions and compactly supported ones. Surjectivity and range characterization issues are addressed from the viewpoint of convolution equations.

math.FA↗

arXiv2018

Characterization of continuous endomorphisms in the space of entire functions of a given order

The aim of this paper is to characterize continuous endomorphisms in the space of entire functions of exponential type of order $p>0$. Let $A_p$ denote the space of entire functions of $n$ complex variables $z\in{\mathbb C}^n$ of order $p$ of normal type. We consider an endomorphism $F$ in the space, which is considered to be a DFS-space. We show that there is a unique linear differential operator $P$ of infinite order with coefficients in the space which realizes $F$, that is, $Ff=Pf$ holds for any $f\in A_p$. The coefficients satisfy certain growth conditions and conversely, if a formal differential operator of infinite order with coefficients in $A_p$ satisfy these conditions, then it induces a continuous endomorphism.

math.FA↗